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1 Vol.44, No.1&2 (2017) 1 14 An Interpretation on Structural Realism to Spacetime Used in Big-Bang Cosmology Is Space Really Expanding? Sho FUJITA Abstract This paper discusses a philosophical answer about the question in relativistic cosmology, is space really expanding? In general cosmology which is called a big-bang theory, cosmological space is said to have been expanding like a balloon gradually pumped up since a big-bang, which is shown by a co-moving coordinate of which the scale gets bigger as a proper time of observers in the earth passes. In this paper, I would like to interpret this phenomenon from a structural spacetime realism s viewpoint in which spacetime is real as different whole structures for different coordinates you arbitrarily choose depending only on a metric/gravitational field. Through my remark, I get a new conclusion of what spacetime really means,thus the role of specetime in contemporary physics fujita@tap.scphys.kyoto-u.ac.jp substantivalism 1

2 relationism structural spacetime realism 1) substance 2. substantivalism relationism , 3) 1) 4) 2

3 Vol. 44 No. 1& Worral (1989) p (2015) 5) p these are merely names of the images we substituted for the real objects which Nature will hide for ever from our eyes. The true relations between these real objects are the only reality we can attain... Poincaré (1905) pp ). 4 the best of both worlds 7) 5 8) 6 individual 7 Ladyman (1998) 9) p. 420 unobservable object supervenient French and Ladyman 12) p matter substance 16) 17) 6 Ladyman (1998) 9), French (1998) 10), (1999) 11), French and Ladyman (2003) 12) 7 French and Ladyman (2003) 12) p Floridi ) Chakravartty ), Psillos ) 3

4 matter G R μν 1 gμνr =8πGTμν (1) 2 1 T μν R μν R ds 2 = g μνdx μ dx ν (2) metric field 11 matter identity μ, ν 0 3 x 0 = t, x 1 = x, x 2 = y, x 3 = z g 00 =1,g 11 = g 22 = g 33 = 1, g ij =0 12 (Dorato ) p. 1610) Dorato 1) p substance substantivalism relationism diffeomorphism 12 Dorato (2008) 18) T μν t μν 4

Vol. 44 No. 1&2 5 Dorato (2000) p. 1610 1) moderate 15 manifold 1 primitive identity 16 structure relation 1 A B 2 1 4 2 17 3 15 19) 16 20) 17 g 0α =0 α 1 3 4 21) [pp.

5 Vol. 44 No. 1&2 5 Dorato (2000) p ) moderate 15 manifold 1 primitive identity 16 structure relation 1 A B ) 16 20) 17 g 0α =0 α ) [pp A B t 1 (x, y, z) t 2 3 (x, y, z) t t 1 C(x, y, z) t 2 D(x, y, z) 320] 18 t 1 t 2 (x, y, z) 3 4 (t 1,x,y,z) (t 2,x,y,z) 3 4 (t 1,x,y,z) (t 2,x,y,z) 5

6 t 1 t 2 (x, y, z) C D C D manifoldmetric identity relation primitive identity 3 22)

Vol. 44 No. 1&2 7 Einstein (1917) 23) 2. 23) 3. 24) Gamov (1948) 25) 4. Penzias and Wilson (1965) 26) 5. Guth (1981) 27) 20 19 Weinberg (1984) pp.

7 Vol. 44 No. 1&2 7 Einstein (1917) 23) 2. 23) 3. 24) Gamov (1948) 25) 4. Penzias and Wilson (1965) 26) 5. Guth (1981) 27) Weinberg (1984) pp ) [ ] ds 2 =c 2 dt 2 a 2 dr 2 (t) 1 Kr 2 +r2 (dθ 2 +sin 2 θdφ 2 ). (3) t 3 (r, θ, φ) 4 (t, r, θ, φ) 3 K 19 3 t a(t) a(t) t a(t) t =0 a(0) = 0 20 t ) 7

8 2017 3.2 3 22 3 a(t) 22) [p. 2] 23 a(t) 3 a(t) 1. manifoldmetric 22 a(t) 22) [pp.

8 a(t) 22) [p. 2] 23 a(t) 3 a(t) 1. manifoldmetric 22 a(t) 22) [pp ] 23 4 t 1 X1: a(t 1 )(r c,θ c,φ c) t 2 X2: a(t 2 )(r c,θ c,φ c) 3 (r c,θ c,φ c) identity relation primitive identity t 1 t 2 2 a(t 1)(r c,θ c,φ c) a(t 2)(r c,θ c,φ c) a(t) 8

9 Vol. 44 No. 1& (r c,θ c,φ c) 1 3 (r, θ, φ) a(t)r = r (r,θ,φ) 3 ds 2 =(c 2 H 2 (t)r 2 )dt 2 +2H(t)dtdr dr 2 1 Kr 2 a 2 (t) r 2 (dθ 2 +sin 2 θdφ 2 ) (4) H(t) H(t) = a(t) a(t) a(t) a(t) t 1 a(t) dtdr H(t) =0 24 t t 4 t K t a(t) K a(t) 4 K 3 a(t) (r,θ,φ) ) [p. 264] 25 3 K>0 3 K <0 28) [p. 45] t 3 a(t) 3 K a(t) K 1 (r c,θ c,φ c) 4 2 X1 X K 3 K 0 a(t) 9

10 (r c,θ c,φ c) T μν vacuum ) 10

11 Vol. 44 No. 1& ) R μν 1 gμνr +Λgμν =8πGTμν (5) 2 1 Λg μν ) [pp ] ) R μν 1 gμνr =8πG(Tμν Λ 2 8πG gμν) =8πG T μν (6) T μν Λ 30 a(t) ) 30 6 T μν Λ 31 30, 31) 11

12 substance 5. 1) substantivalism

13 Vol. 44 No. 1& Mauro Dorato (2000) Substantivalism, Relationism, and Structural Spacetime Realism. Foundations of Physics, 30, , Plenum Publishing Corporation. 2 Carl Hoefer (1996) The Metaphysics of Space- Time Substantivalism. The Journal of Philosophy, Vol.93, No.1, pp Paul Teller (1991) Substance, Relations, and Arguments about the Nature of Space-Time. The Philosophical Review, Vol.100, No.3 (July 1991), pp (2016). 37, pp (2015).. 6 Jules-Henri Poincaré (1905) Science and Hypothesis. (Page references to the Dover reprint of the first English translation of 1905). 7 John Worral (1989) Structural realism. Dialectica, 43, pp Newman, M. H. A. (1928) Mr. Russell s Causal Theory of Perception. Mind, Vol.37, No.146 (Apr. 1928), pp James Ladyman (1998) What is Structural Realism?. Studies In History and Philosophy of Science Part A, Vol.29, No.3. (September 1998), pp Steven French (1998) On the whithering away of physical objects Princeton University Press, pp Steven French (1999) Models and mathematics in physics: The role of group theory Cambridge University Press, pp Steven French and James Ladyman (2003) Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure. Synthese, Volume 136, Issue 1, pp Luciano Floridi (2008) A defence of informational structural realism Synthese March 2008, Volume 161, Issue 2, pp Anjan Chakravartty (2003) The Structuralist Conception of Objects Philosophy of Science, 70, pp Stathis Psillos (2006) The Structure, the Whole Structure and Nothing But the Structure? Philosophy of Science, 73, pp Albert Einstein, Leopold Infeld and Beate Hoffmann (1938) The Gravitational Equations and the Problem of Motion Annals of Mathematics Second Series, Vol.39, No.1 (Jan. 1938), pp Andrei Sakharov (1991) Vacuum quantum fluctuations in curved space and the theory of gravitation American Institute of Physics Soviet Physics Uspekhi, Volume 34, Number Mauro Dorato (2008) Is Structural Spacetime Realism Relationism in Disguise? The Supererogator ynature of the Substantivalism/Relationism Debate Philosophy and Foundations of Physics, Volume 4, (2008) 19 Michael Esfeld and Vincent Lam (2006) Moderate structural realism about space-time. Springer Science+Business Media B.V. 20 Robert Adams (1979) Primitive Thisness and Primitive Identity The Journal of Philosophy, Vol.76, No.1 (January 1979), pp ,, (1978).. 22 Steven Weinberg (1984) COSMOLOGY OXFORD UNIVERSITY PRESS. 23 Albert Einstein (1917) Kosmologische Betrachtungen zur allgemeinen Relativitatstheories. Koniglicb Preußiscbe Akademie der Wissenscbaften, Sitzungsbericbte, pp Edwin Hubble (1929) A relation between distance and radial velocity among extra-galactic nebulae National Academy of Sciences Vol.15 No.3, pp George Gamov (1948) The Origin of Elements and the Separation of Galaxies. reprinted in Bernstein 13

14 and Feinberg, pp Arno A Penzias and Robert W Wilson (1965) A Measurement of Excess Antenna Temperature at 4080 Mc/s. reprinted in Bernstein and Feinberg (1986), pp Alan H Guth (1981) A Possible Soluton to the Horizon and Flatness Problems. reprinted in Bernstein and Feinberg (1986), pp (2010).. 29 Adam G Riess and Alexei V Filippenko, Peter Challis et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, Volume 116, Number Jeremy Butterfield and Chris Isham (1999) Spacetime and the Philosophical Challenge of Quantum Gravity. from Physics Meets Philosophy at the Planck Scale: Contemporary Theories in quantum gravity edited by Craig Callender, Nick Huggett (2001) Cambridge University Press. 31 Daniele Oriti (2009) Approaches to quantum gravity: Toward a new understanding of space, time, and matter. Cambridge University Press. 32 Katsuhiko Sato (1981) First-order phase transition of a vacuum and the expansion of the Universe. The Royal Astronomical Society.Provided by the NASA Astrophysics Data System. 33 (2007)

Abstract Although physicalism is usually understood as an ontological thesis, it is not clear that what implications this position has on th

Abstract Although physicalism is usually understood as an ontological thesis, it is not clear that what implications this position has on th Title スーパーヴィーニエンステーゼと存在論的コミットメント : 物理主義の存在論的含意の把握に向けて Author(s) 井頭, 昌彦 Citation 科学哲学, 42(2): 59-73 Issue 2009-10 Date Type Journal Article Text Version publisher URL http://hdl.handle.net/10086/22102